Search Results for Levi-Civita

Biographies

Two of his teachers were Giuseppe Veronese and Ricci-Curbastro and Levi-Civita later collaborated with the latter.

By putting together Ricci-Curbastro's algorithm with some results from Lie's theory of transformation groups, Levi-Civita extended the theory of absolute invariants to more general cases than those considered by Ricci-Curbastro.

Levi-Civita was appointed to the Chair of Rational Mechanics at Padua in 1898, a post which he was to hold for 20 years.

In particular in 1909 Castelnuovo tried hard to persuade him to move, but Levi-Civita was happy to remain in Padua.

Levi-Civita was a pacifist with firm socialist ideas and it may well have been that he felt Padua suited his personality better than Rome at the time.

Levi-Civita was always very international in his outlook and the ability of Rome to attract top quality students from abroad must have figured in his reasons to now want to make the move there.

Levi-Civita was opposed to such ideas as he made clear in a letter he wrote to Sommerfeld in 1920:-
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When Von Karman approached Levi-Civita in 1922 suggesting a scientific meeting on fluid dynamics he knew that such a meeting could not be an official congress if German and Italian scientists were both involved so he proposed an informal one.

Levi-Civita was enthusiastic but when the meeting took place in Innsbruck in September of that year the only scientists from the Allied Powers to participate were Levi-Civita and members of his research group.

Levi-Civita's role is described in detail by Battimelli in [Riv.

Tullio Levi-Civita was one of the leading figures in the creation, in the years following World War I, of the International Congresses of Applied Mechanics, and remained an active member of the Congress committee to the end of his life.

Levi-Civita [made a major] contribution to the life of the Congresses, from the early days of the 1922 Innsbruck conference to the late thirties [with] his role in the international network created by the newborn institution ..

It was not just the international situation which gave Levi-Civita problems but also the effect of totalitarianism and anti-Semitism on scientific and university life.

Although he was deeply opposed to such ideas, Levi-Civita felt that for the sake of his family and his research school in Rome he had to sign despite his strong moral objections.

Later in 1936 the International Mathematical Congress was held in Oslo but Levi-Civita, and all other Italian mathematicians, were forbidden to attend by their government.

Despite this Levi-Civita was appointed as a member of the Commission for awarding Fields Medals.

Levi-Civita was dismissed from his professorship, forced to leave the editorial board of Zentralblatt fur Mathematik, and prevented from attending the Fifth International Congress of Applied Mechanics in the United States.

In the last years of his life, in spite of his moral and physical depression, Levi-Civita remained faithful to the ideal of scientific internationalism and helped colleagues and students who were victims of anti-Semitism; thanks to him, many of them found positions in South America or in the USA.

Levi-Civita had very great command of pure mathematics, with particularly strong geometric intuition which he applied to a variety of problems of applied mathematics.

The paper was requested by Klein when he met Levi-Civita in Padua in 1899 and, following Klein's wishes, it appeared in Mathematische Annalen.

Weyl was to take up Levi-Civita's ideas and make them into a unified theory of gravitation and electromagnetism.

Levi-Civita's work was of extreme importance in the theory of relativity, and he produced a series of papers elegantly treating the problem of a static gravitational field.

This topic was discussed in a correspondence between Levi-Civita and Einstein.

the main mathematical and physical questions discussed by Einstein and Levi-Civita in their 1915 - 1917 correspondence: the variational formulation of the gravitational field equations and their covariance properties, and the definition of the gravitational energy and the existence of gravitational waves.

Analytic dynamics was another topic studied by Levi-Civita, many of his papers examining special cases of the three-body problem.

In 1950 (nine years after his death) a book by Levi-Civita entitled Le probleme des n corps en relativite generale was published.

In [Italian mathematics between the two world wars (Pitagora, Bologna, 1987), 125-141.',18)">18] the authors argue that Levi-Civita was interested in the theory of stability and qualitative analysis of ordinary differential equations for three reasons: his interest in geometry and geometric models; his interest in classical mechanics and celestial mechanics, in particular, the three-body problem; and his interest in stability of movement in the domain of analytic mechanics.

Levi-Civita's interest in hydrodynamics began early in his career with his paper Note on the resistance of fluids appearing in 1901.

The leading mathematicians of the day were members, for example in the early years of the 20th century Henri Poincare, Jacques Hadamard, David Hilbert, Vito Volterra, Federigo Enriques, Guido Castelnuovo, Corrado Segre, Giuseppe Peano, Tullio Levi-Civita, Gregorio Ricci-Curbastro and Luigi Bianchi were members.

However, despite being ranked first, Pavia did not appoint Nalli to the chair and she wrote a strong letter of complaint to the rector of the university as well as writing to Tullio Levi-Civita complaining bitterly about the injustice.

We do not know what reply she had from Levi-Civita but he seems to have given her encouragement since, in February 1927, she was took up an appointment as professor at the University of Catania.

However, the greatest indication of the reply Nalli must have received is seen from the fact that at this time she changed her research topic and after this worked on tensor calculus, the topic for which Levi-Civita is famed.

In 1915 he discovered the Levi-Civita connection in Riemannian manifolds independently of Levi-Civita but since his paper only appeared in 1919, a year later than Levi-Civita's, he received no credit.

Up to the point when he saw Giovanni Ricci's and Tulio Levi-Civita's work, Schouten's notation had been, by his own admission, difficult to understand but, once he saw their notation he accepted it immediately as simpler than his own.

Although both authors appear on both volumes (each dedicated to Tullio Levi-Civita), the first volume is largely the work of Schouten while the second is largely the work of Struik.

Much of Ricci-Curbastro's work after 1900 was done jointly with his student Levi-Civita.

In the paper, applications are given by Ricci-Curbastro and Levi-Civita to the classification of the quadratic forms of differentials and there are other analytic applications; they give applications to geometry including the theory of surfaces and groups of motions; and mechanical applications including dynamics and solutions to Lagrange's equations.

1 (1926), 555-567.',7)">7], written by Ricci-Curbastro's student Levi-Civita, lists sixty-one of his publications.

She met Emmy Noether, who she would later pay tribute to in her article Portraits of women mathematicians, and in Rome during the winter term of 1930-31 she met Levi-Civita who was working on similar problems in fluid mechanics which interested her [l\'Annuaire des Anciens Eleves de l\'Ecole Normale Superieure (1972).

Levi-Civita, surprised and interested, encouraged her to continue her studies.

She established the existence of an infinity of waves, those of Gerstner and Levi-Civita being two examples.

In fact Vitali was only ranked as second choice by the referees (although Fubini and Levi-Civita had ranked him top), but the candidate who came top, Gustavo Sannia, did not accept the post when offered it.

Disliking the small university atmosphere of Illinois, he returned within a few months to Gottingen, going next to Italy at the invitation of Levi-Civita.

Einstein also argued about relativity in a correspondence with Levi-Civita and Abraham played a role in this argument too, see for example [Italian mathematics between the two world wars (Bologna, 1987), 143-159.',4)">4].

He wrote important papers which contributed to the development of the tensor calculus of C G Ricci-Curbastro and Tullio Levi-Civita.

Indeed this influence is clearly seen since this allowed Ricci-Curbastro and Levi-Civita to develop a coordinate free differential calculus which Einstein, with the help of Grossmann, turned into the tensor analysis mathematical foundation of general relativity.

In Rome Vrănceanu studied under Levi-Civita, obtaining his doctorate on 5 November 1924 for a dissertation Sopra una teorema di Weierstrass e le sue applicazioni alla stabilita which gave a new proof of a theorem on the decomposition of analytical functions of more variables and also studied applications of the theorem to mechanics.

Vrănceanu returned to Iasi and, in 1926, still developing ideas suggested by Levi-Civita, Vrănceanu discovered the notion of a non-holonomic space.

The leading mathematicians of the day were members, for example in the early years of the 20th century Henri Poincare, Jacques Hadamard, David Hilbert, Vito Volterra, Federigo Enriques, Guido Castelnuovo, Corrado Segre, Giuseppe Peano, Tullio Levi-Civita, Gregorio Ricci-Curbastro and Luigi Bianchi were members.

He was able to get support for his position from many leading mathematicians such as the Germans Edmund Landau and Hermann Weyl, the Frenchmen Maurice Frechet and Jacques Hadamard, the American George D Birkhoff, and the Italians Gaetano Scorza, Luigi Bianchi, Tullio Levi-Civita, Francesco Severi, and Vito Volterra.

These were Giuseppe Veronese, who held the Chair of Algebraic Geometry, Tullio Levi-Civita, who had been appointed to the Chair of Rational Mechanics in 1898, a post which he held for 20 years, and Francesco Severi, who had been appointed to the Chair of Projective and Descriptive Geometry in 1905.

Cherubino was awarded a government scholarship for advanced study which allowed him to attend the courses of Levi-Civita and Veronese while, advised by Severi, he devoted himself to the study of algebraic geometry.

',2)">2] Dell'Aglio looks at the approaches of Levi-Civita, Painleve and Sundman to the three body problem which:-
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it is possible to show the existence of two different research programs, one related to Levi-Civita's works, the other to Sundman's investigations, which include for the first time a complete regularization of the three-body problem.

He entered the university and, together with some fellow students who also were keen to learn about differential geometry and Riemannian geometry, he studied some of the major texts such as those by Schouten, Weyl, Eisenhart, Levi-Civita and Cartan.

He was in Korea for the Symposium on Differential Geometry at Seoul and Kyunpook Universities from 14 to 18 September, then he was in Rome to celebrate the 100th birthday of Levi-Civita at the Accademia Nazionale dei Lincei in December.

About 1912, Einstein began a new phase of his gravitational research, with the help of his mathematician friend Marcel Grossmann, by expressing his work in terms of the tensor calculus of Tullio Levi-Civita and Gregorio Ricci-Curbastro.

In the same year he entered the University of Padua where he studied pure mathematics, taught by a number of excellent teachers including Gregorio Ricci-Curbastro, Tullio Levi-Civita, Giuseppe Veronese, and Francesco Severi who was appointed to Padua in 1905 when Comessatti was in his second year of study [Rend.

He submitted his thesis Despre invariantii adiabatici ai sistemelor neoronome in 1932 and he defended it before a committee chaired by Levi-Civita and eleven other professors including Vito Volterra who was a good friend of Romanian mathematicians.

It was Grossmann who pointed out to him the relevance to general relativity of the tensor calculus which had been proposed by Elwin Bruno Christoffel in 1864, and developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita around 1901.

The year in Italy was an extremely profitable time for Roth, for there he met many of the great Italian mathematicians and he learnt a great deal from Castelnuovo, Enriques, and Levi-Civita in addition to Severi.

C Cattani, Levi-Civita's influence on Palatini's contribution to general relativity, in The attraction of gravitation: new studies in the history of general relativity, Johnstown, PA, 1991 (Birkhauser Boston, Boston, MA, 1993), 206-222.

C Cattani and M De Maria, Einstein's path toward the generally covariant formulation of gravitational field equations: the contribution of Tullio Levi-Civita, in Proceedings of the fourth Marcel Grossmann meeting on general relativity, Part A, B, Rome, 1985 (North-Holland, Amsterdam, 1986), 1805-1826.

L Dell'Aglio, The role of applications in the works of Levi-Civita, Riv.

L Dell'Aglio and G Israel, The themes of stability and qualitative analysis in the works of Levi-Civita and Volterra (Italian), Italian mathematics between the two world wars (Pitagora, Bologna, 1987), 125-141.

C Cattani and M De Maria, Einstein's path toward the generally covariant formulation of gravitational field equations : the contribution of Tullio Levi-Civita, in Proceedings of the fourth Marcel Grossmann meeting on general relativity (Amsterdam-New York, 1986), 1805-1826.

C Cattani and M De Maria, Gravitational waves and conservation laws in general relativity : A Einstein and T Levi-Civita, 1917 correspondence, in Proceedings of the Fifth Marcel Grossmann Meeting on General Relativity (Teaneck, NJ, 1989), 1335-1342.

C Cattani and M De Maria, The 1915 epistolary controversy between Einstein and Tullio Levi-Civita, in Einstein and the history of general relativity (Boston, MA, 1989), 175-200.

Tullio Levi-Civita, Honorary Member of the Edinburgh Mathematical Society, was born at Padua on March 29th, 1873, and died in Rome on December 29th, 1941.

Levi-Civita's work as a mathematician is notable for its quality, quantity and range.

Ricci-Curbastro and Levi-Civita together developed this theory, and in 1901 published a joint memoir, "Methodes du calcul differentiel absolu et leurs applications" in the Mathematische Annalen (vol.

Originally it was a technique rather than a separate branch of mathematics, providing as it did a way of writing theorems of differential geometry and the calculus in a form at once concise and general, and it was not until after the development of relativity, followed shortly afterwards by Levi-Civita's definition of parallelism in Riemannian geometry, that it assumed the full place it now holds as one of the main branches of modern mathematics.

This discovery by Levi-Civita, together with the contemporary development of general relativity and the search for a unified theory of gravitation and electromagnetism by Weyl, Eddington, Einstein and others, quickly led to generalisations of Riemannian geometry.

In 1870 Felix Klein had defined a geometry to be the invariant theory of a transformation group, a definition which included such geometries as Euclidean, affine and projective, but did not include Riemannian, In the light of Levi-Civita's definition of parallelism it was seen that the spaces of differential geometry could, so to speak, be regarded as an assemblage of isomorphic, Klein spaces, each associated with a point of an "underlying space," and in this way there grew an extensive literature directly inspired by the work of Levi-Civita.

Levi-Civita himself, it is true, made no special contribution to these developments and it seems not unlikely that many of them could have held little interest for him being too far removed from the simple directness of his own work.

By his early work with Ricci on tensor analysis and by his later discovery of infinitesimal parallelism, Levi-Civita laid the foundations both for relativity and for the establishment of differential geometry as one of the great branches of modern mathematics.

Tullio Levi-Civita, Honorary Member of the Edinburgh Mathematical Society, was born at Padua on March 29th, 1873, and died in Rome on December 29th, 1941.

Levi-Civita's work as a mathematician is notable for its quality, quantity and range.

Ricci-Curbastro and Levi-Civita together developed this theory, and in 1901 published a joint memoir, "Methodes du calcul differentiel absolu et leurs applications" in the Mathematische Annalen (vol.

Originally it was a technique rather than a separate branch of mathematics, providing as it did a way of writing theorems of differential geometry and the calculus in a form at once concise and general, and it was not until after the development of relativity, followed shortly afterwards by Levi-Civita's definition of parallelism in Riemannian geometry, that it assumed the full place it now holds as one of the main branches of modern mathematics.

This discovery by Levi-Civita, together with the contemporary development of general relativity and the search for a unified theory of gravitation and electromagnetism by Weyl, Eddington, Einstein and others, quickly led to generalisations of Riemannian geometry.

In 1870 Felix Klein had defined a geometry to be the invariant theory of a transformation group, a definition which included such geometries as Euclidean, affine and projective, but did not include Riemannian, In the light of Levi-Civita's definition of parallelism it was seen that the spaces of differential geometry could, so to speak, be regarded as an assemblage of isomorphic, Klein spaces, each associated with a point of an "underlying space," and in this way there grew an extensive literature directly inspired by the work of Levi-Civita.

Levi-Civita himself, it is true, made no special contribution to these developments and it seems not unlikely that many of them could have held little interest for him being too far removed from the simple directness of his own work.

By his early work with Ricci on tensor analysis and by his later discovery of infinitesimal parallelism, Levi-Civita laid the foundations both for relativity and for the establishment of differential geometry as one of the great branches of modern mathematics.

Under the influence of the Norwegian school she became interested in the mathematical theory of waves in ideal liquids, in particular in the work of Levi-Civita.

At her first meeting with the renowned Levi-Civita, she told him about an important difference between the irrotational wave he had just described (of a ideal liquid with a free surface) and a rotational wave which Gerstner had described a long time before (the cycloidal wave).

Levi-Civita, surprised and interested, encouraged her to continue her studies.

She established the existence of an infinity of waves, those of Gerstner and Levi-Civita being two examples.

Quotations

Chronology

Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.

Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.

Levi-Civita and Ricci-Curbastro publish Methodes de calcul differential absolu et leures applications in which they set up the theory of tensors in the form that will be used in the general theory of relativity 15 years later.